How do you solve $|b | - 2< 89$ ?

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How do you solve $|b | - 2< 89$ ?

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Answer 1 · 2017-09-27T21:31:29

First, add $2$ to both sides: $|b| < 91$ .

So, we know that $b$ is less than $91$ and greater than $-91$ .

Thus, $b$ < 91 and b > -91.

$(-91, 91)$

Answer 2 · 2017-09-27T21:31:49

See a solution process below:

Explanation:

First, add $color(red)(2)$ to each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

$abs(b) - 2 + color(red)(2) < 89 + color(red)(2)$

$abs(b) - 0 < 91$

$abs(b) < 91$

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

$-91 < b < 91$

Or

$b > -91$ and $b < 91$

Or, in interval notation:

$(-91, 91)$

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How do you solve $|b | - 2< 89$ ?

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